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78                            BYZANTINE CHURCHES                        CHAP.
and compares favourably with the methods employed elsewhere to apply the dome to the octagon.1 In the octagonal church of S. Lorenzo at Milan the octagon is turned into the circle by the introduction of squinches. In San Vitale a considerable walling is built between the line of the octagon and the springing line of the dome3 while the bed for the dome is formed by introducing, in the space over the angles of the octagon, niches which are worked above to the circle on plan. On the other hand3 it is interesting to compare with these methods the method employed in the baptistery of S. Sophia5 now a Sultan's Turb65 near the southern entrance to the inner narthex. Although the walls of the building describe a square on the exterior, they form an octagon on the interior with semicircular bays at the diagonals, as in SS. Sergius and Bacchus. But in the application of the dome the true pendentive is used. The baptistery was erected shortly before S. Sophia, and in view of the erection of the great church.
The curvature of the dome of SS. Sergius and Bacchus has three zones, which have respectively a radius of m. 8, (drawn from the centre of the octagon), m. 3^, and m. 9^ (centre about m. 2, below the springing of the dome). The first extends to a point a little above the heads of the dome windows ; the second about m. 2 higher ; the third to the crown of the dome. The groins stop short a little below the dome's apex, where they are arched into one another, leaving a saucer-shaped crown now capped by a Turkish finial. The dome is covered with lead, and presents an undulating surface owing to the protuberance of its eight concave compartments.2
1  In S, George of Ezra in Syria '(515), as Mr. E. M. Antoniadi informs me, the dome overhangs or oversails the angles of the octagon.
2  * The dome stands within a polygon of sixteen sides, that rises four metres above the springing line, keeping the dome taut and weighting the haunches, Against this polygonal casing are set buttresses formed by the extension of the piers of the octagon to within m, x from the cornice of the dome.   These buttresses are in their turn respectively strengthened, on the rear, by two small buttresses ; of which those on the north, south, east, and west sides rest on an arch of the gynecaeum, and carry the thrust to the outer walls of the church, while the others rest on the exhedrae and the vaulting of the gynecaeum.    Furthermore, from the summit of the buttresses formed by the piers of the octagon a small buttress is set against the cupola itself up to the cornice.'   This marshalling of the